Make the Dough. In a large bowl, whisk together the flour, sugar, and salt. Add cold cubed butter and use a pastry cutter (or your hands) to mix until crumbly. Add the egg and a tablespoon of milk or water at a time, mixing just until the dough comes together. Divide into two disks, wrap in plastic, and chill for 30 minutes.
Roll & Cut. Preheat the oven to 375°F. On a lightly floured surface, roll out one dough disk into a rectangle about 1/8-inch thick. Cut into evenly sized rectangles (about 3x4 inches).
Add the Filling. Place half the rectangles on a parchment-lined baking sheet. Add 1 to 2 teaspoons of jam to the center of each. Top with the remaining dough rectangles. Press edges with a fork to seal, and poke a few holes in the top for steam.
Bake. Brush each pop tart with a beaten egg. Bake for 20–25 minutes or until golden brown. Let cool completely before icing.
Glaze and Decorate. Whisk powdered sugar, a splash of milk, and vanilla extract to make the glaze. Spread over cooled pop tarts and top with sprinkles if using. Let glaze set for 15 minutes before serving.